For every k ≥ 4 the map p to the natural density of integers whose k-th smallest prime divisor is p fails to be unimodal.
Dusart,Estimates of some functions over primes without R.H
2 Pith papers cite this work. Polarity classification is still indexing.
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For large primes p, the least consecutive pair of primitive roots u and u+1 (u not ±1 or a square) satisfies u ≪ O((log p)^2 (log log p)^5).
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A Complete Answer to Erd\H{o}s Problem 690
For every k ≥ 4 the map p to the natural density of integers whose k-th smallest prime divisor is p fails to be unimodal.
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Least Consecutive Pair of Primitive Roots
For large primes p, the least consecutive pair of primitive roots u and u+1 (u not ±1 or a square) satisfies u ≪ O((log p)^2 (log log p)^5).